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Metacognition and motivation as predictors for mathematics performance of Belgian elementary school children

  • Annemie DesoeteEmail author
  • Elke Baten
  • Vera Vercaemst
  • Ann De Busschere
  • Myriam Baudonck
  • Jennis Vanhaeke
Original Article

Abstract

In this paper, we investigate the role of metacognitive postdiction skills, intrinsic motivation and prior proficiency in mathematics as Propensity factors within the opportunity–propensity (O–P) model of learning. We tested Belgian children from Grade 1 till 6 in January and June. The study revealed overlapping yet different predictors for mathematical accuracy and fluency, which led us to the practical recommendation for teachers to pay attention to both aspects of mathematics. The metacognitive postdiction skills of children were related to accuracy in mathematics during the whole elementary school period. In addition, we observed that children evaluated their own performance as worse when they were slower in Grades 3 and 4. Intrinsic motivation was related to accuracy but not to fluency in Grade 3. Especially prior mathematical accuracy mattered as a propensity factor. More than half of the variance in accuracy and less than one-fifth of the variance in fluency in January predicted the performances of children for mathematics in June, a finding that highlights the importance of longitudinal designs including students’ prior mathematical accuracy’ as well. Finally, we observed that poor mathematics performers are less intrinsically motivated, and less metacognitively accurate. Moreover, they overestimate their performances more often than well-performing peers in all grades, stressing the importance of paying attention to these aspects in mathematics education.

Keywords

Metacognitive postdiction Metacognitive accuracy Intrinsic motivation Prior knowledge Mathematical accuracy Mathematical fluency Overestimation 

References

  1. Aesaert, K., & Denis, J. (2018). Evolutie wiskundeprestaties in het lager onderwijs Trendanalyse van peilingsdata tussen 2002 en 2016 [Evolution of mathematics performances in elementary school children. Trend analysis of testing between 2002 and 2016]. Paper on the Studie-en ontmoetingsdag voor Vlaamse onderzoekers, opleiders en begeleiders van het wiskundeonderwijs aan 3- tot 14-jarigen [Research meeting for Flemish researchers, trainers and educators to 3 till 14-years olds]. 5 June 2018 KULeuven campus groep T (Leuven: Belgium). https://ppw.kuleuven.be/o_en_o/CIPenT/studiedag-wiskundeonderwijs-2018/presentaties/k-aesaert.
  2. Arefi, M., Naghibzadeh, M., & Boloki, A. (2014). The relationship of parental attachment, peer attachment, and academic self-concept to academic achievement of high school students. International Journal of Academic Research, 6, 73–78.Google Scholar
  3. Baten, E., & Desoete, A. (2018). Mathematical (dis)abilities within the opportunity–propensity model: The choice of mathematics test matters. Frontiers in Psychology, Developmental Psychology.  https://doi.org/10.3389/fpsyg.2018.00667.Google Scholar
  4. Baten, E., Praet, M., & Desoete, A. (2017). The relevance and efficacy of metacognition for instructional design in the domain of mathematics. ZDM Mathematics Education, 49, 613–623.  https://doi.org/10.1007/s11858-017-0851-y.Google Scholar
  5. Baudonck, M., Debusschere, A., Dewulf, B., Samyn, F., Vercaemst, V., & Desoete, A. (2006). De Kortrijkse Rekentest Revision KRT-R. [The Kortrijk Arithmetic Test Revision KRT-R]. Kortrijk: CAR Overleie.Google Scholar
  6. Boekaerts, M., & Rozendaal, J. S. (2010). Using multiple calibration indices in order to capture the complex picture of what affects students’ accuracy of feeling of confidence. Learning and Instruction, 20, 372–382.Google Scholar
  7. Bol, L., & Hacker, D. J. (2012). Calibration research: Where do we go from here? Frontiers in Psychology, 3, 1–6.Google Scholar
  8. Borkowski, J. G. (1992). Metacognitive theory: A framework for teaching literacy, writing, and mathematics skills. Journal of Learning Disabilities, 25, 253–257.Google Scholar
  9. Borkowski, J. G., & Thorpe, P. K. (1994). Self-regulation and motivation: A life-span perspective on underachievement. In D. H. Schunk & B. J. Zimmerman (Eds.), Selfregulation of learning and performance: Issues of educational applications (pp. 45–100). Hillsdale: Erlbaum.Google Scholar
  10. Brown, A. (1987). Metacognition, executive control, self-regulation, and other more mysterious mechanisms. In F. Reiner & R. Kluwe (Eds.), Metacognition, motivation, and understanding (pp. 65–116). Hillsdale: Lawrence Erlbaum.Google Scholar
  11. Byrnes, J. P., & Miller, D. C. (2007). The relative importance of predictors of mathematics and science achievement: An opportunity–propensity analysis. Contemporary Educational Psychology, 32, 599–629.  https://doi.org/10.1016/j.cedpsych.2006.09.002.Google Scholar
  12. Byrnes, J. P., & Wasik, B. A. (2009). Factors predictive of mathematics achievement in kindergarten, first and third grades: An opportunity–propensity analysis. Contemporary Educational Psychology, 34, 167–183.  https://doi.org/10.1016/j.cedpsych.2009.01.002.Google Scholar
  13. Carr, M., Alexander, J., & Folds-Bennett, T. (1994). Metacognition and mathematics strategy use. Applied Cognitive Psychology, 8, 583–595.  https://doi.org/10.1002/acp.2350080605.Google Scholar
  14. Carr, M., & Jessup, D. L. (1995). Cognitive and metacognitive predictors of mathematics strategy use. Learning and Instruction, 7, 235–247.  https://doi.org/10.1016/1041-6080(95)90012.Google Scholar
  15. Chen, P. P. (2002). Exploring the accuracy and predictability of the self-efficacy beliefs of seventh-grade mathematics students. Learning and Individual Differences, 14, 77–90.Google Scholar
  16. Claessens, A., Duncan, G., & Engel, M. (2009). Kindergarten skills and fifth-grade achievement: Evidence from the ECLS-K. Economics of Education Review, 28, 415–427.  https://doi.org/10.1016/j.econedurev.2008.09.003.Google Scholar
  17. Claessens, A., & Engel, M. (2013). How important is where you start? Early mathematics knowledge and later school success. Teachers College Record, 115(6), 060306.Google Scholar
  18. Cohen Kadosh, R., & Dowker, A. (2015). The Oxford handbook of numerical cognition. Oxford: Oxford University Press.Google Scholar
  19. Deary, I. J., Whalley, L. J., Lemmon, H., Crawford, J. R., & Starr, J. M. (2000). The stability of individual differences in mental ability from childhood to old age: Follow-up of the 1932 Scottish mental survey. Intelligence, 28, 49–55.  https://doi.org/10.1016/S0160-2896(99)00031-8.Google Scholar
  20. Deci, E. L., Conell, J., & Ryan, R. (1989). Self determination in a work organization. Journal of Applied Psychology, 74(4), 580–590.Google Scholar
  21. Deci, E. L., & Ryan, R. M. (1985). Intrinsic motivation and self-determination in human behavior. Boston: Springer US.  https://doi.org/10.1007/978-1-4899-2271-7.Google Scholar
  22. Desender, K., Van Opstal, F., & Van den Bussche, E. (2017). Subjective experience of difficulty depends on multiple cues. Scientific Reports, 7, 44222.  https://doi.org/10.1038/srep44222.Google Scholar
  23. Desoete, A. (2007). Evaluating and improving the mathematics teaching–learning process through metacognition? Electronic Journal of Research in Educational Psychology, 5, 705–730.Google Scholar
  24. Desoete, A. (2008). Multi-method assessment of metacognitive skills in elementary school children: How you test is what you get. Metacognition Learning, 3, 189–206.  https://doi.org/10.1007/s11409-008-9026-0.Google Scholar
  25. Desoete, A., & Roeyers, H. (2002). Off-line metacognition. A domain-specific retardation in young children with learning disabilities? Learning Disability Quarterly, 25, 123–139.  https://doi.org/10.2307/1511279.Google Scholar
  26. Desoete, A., & Roeyers, H. (2006). Metacognitive macroevaluations in mathematical problem solving. Learning and Instruction, 16, 12–25.  https://doi.org/10.1016/j.learninstruc.2005.12.003.Google Scholar
  27. Desoete, A., Roeyers, H., & Buysse, A. (2001). Metacognition and mathematical problem solving in grade 3. Journal of Learning Disabilities, 34, 435–449.  https://doi.org/10.1177/002221940103400505.Google Scholar
  28. Dowker, A. (2005). Individual differences in arithmetic. Implications for psychology, neuroscience and education. Hove: Psychology Press.Google Scholar
  29. Dowker, A. (2015). Individual differences in arithmetical abilities. The componential nature of arithmetic. In The Oxford Handbook of Mathematical Cognition (pp. 862–878). Oxford: Medicine UK.Google Scholar
  30. Duncan, G. J., & Magnuson, K. (2009). The nature and impact of early achievement skills, attention and behavior problems. Paper presented at the Russel Sage Foundation conference on Social Inequality and Educational Outcomes, November 19–20.Google Scholar
  31. Efklides, A. (2001). Metacognitive experiences in problem solving: Metacognition, motivation, and self-regulation. In A. Efklides, J. Kuhl & R. M. Sorrentino (Eds.), Trends and prospects in motivation research (pp. 297–323). Dordrecht: Kluwer.Google Scholar
  32. Efklides, A. (2006). Metacognition and affect: What can metacognitive experiences tell us about the learning process? Educational Research Review, 1, 3–14.  https://doi.org/10.1016/j.edurev.2005.11.00.Google Scholar
  33. Efklides, A. (2008). Metacognition: Defining its facets and levels of functioning in relation to self-regulation and co-regulation. European Psychologist, 13, 277–287.  https://doi.org/10.1027/1016-9040.13.4.277.Google Scholar
  34. Efklides, A., & Sideridis, G. D. (2009). Assessing cognitive failures. European Journal of Psychological Assessment, 25, 69–72.Google Scholar
  35. Erickson, S., & Heit, E. (2015). Metacognition and confidence: Comparing mathematics to other academic subjects. Frontiers in Psychology.  https://doi.org/10.3389/fpsyg.2015.00742.Google Scholar
  36. Flavell, J. H. (1976). Metacognitive aspects of problem-solving. In L. B. Resnick (Ed.), The nature of intelligence (pp. 231–236). Hillsdale: Erlbaum.Google Scholar
  37. Flavell, J. H. (1979). Metacognition and cognitive monitoring: A new area of cognitive developmental inquiry. American Psychologist, 34, 906–911.Google Scholar
  38. Flavell, J. H. (1987). Speculations about the nature and development of metacognition. In F. E. Weinert & R. Kluwe (Eds.), Metacognition, motivation and understanding (pp. 20–29). Hillsdale: Erlbaum.Google Scholar
  39. Fleming, S. M., Donlan, R. J., & Frith, C. D. (2012). Metacognition: Computation, biology and function. Philosophical Transactions of the Royal Society, 367, 1280–1286.  https://doi.org/10.1098/rstb.2012.0021.Google Scholar
  40. Fleming, S. M., & Lau, H. C. (2014). How to measure metacognition. Frontier in human neuroscience, 8(443), 1–8.  https://doi.org/10.3389/frhum.2014.00443.Google Scholar
  41. Furnes, B., & Norman, E. (2015). Metacognition and reading: Comparing three forms of metacognition in normally developing readers and readers with dyslexia. Dyslexia, 21, 273–284.  https://doi.org/10.1002/dys.1501.Google Scholar
  42. Gagné, M., & Deci, E. L. (2005). Self-determination theory and work motivation. Journal of Organizational Behavior, 26(4), 331–362.  https://doi.org/10.1002/job.322.Google Scholar
  43. García, T., Rodríguez, C., González-Castro, P., González-Pienda, J. A., & Torrance, M. (2016). Elementary students’ metacognitive processes and post-performance calibration on mathematical problem-solving tasks. Metacognition and Learning, 11, 139–170.Google Scholar
  44. Gascoine, L., Higgins, S., & Wall, K. (2017). The assessment of metacognition in children aged 4–16 years: a systematic review. Review of Education, 5, 3–57.  https://doi.org/10.1002/rev3.3077.Google Scholar
  45. Guay, F., Marsh, H. W., & Boivin, M. (2003). Academic self-concept and academic achievement: Developmental perspectives on their causal ordering. Journal of Educational Psychology, 95, 124–136.  https://doi.org/10.1037/0022-0663.95.1.124.Google Scholar
  46. Hacker, J. D., Bol, L., Horgan, D. D., & Rakow, E. A. (2000). Test prediction and performance in a classroom context. Journal of Educational Psychology, 92, 160–170.Google Scholar
  47. Henik, A., Rubinstein, O., & Ashkenazi, S. (2015). Developmental dyscalculia as a heterogenous disability. In R. Cohen, Kadosh & A. Dowker (Eds.), The Oxford handbook of numerical cognition (pp. 662–667). Oxford: Oxford University Press.Google Scholar
  48. Koriat, A. (2007). Metacognition and consciousness. In P. D. Zelazo, M. Moscovitch & E. Thompson (Eds.), The Cambridge handbook of consciousness (pp. 289–325). Cambridge: Cambridge University Press.Google Scholar
  49. Kriegbaum, K., Jansen, M., & Spinath, B. (2015). Motivation: A predictor of PISA’s mathematical competence beyond intelligence and prior test achievement. Learning and Individual Differences, 43, 140–148.  https://doi.org/10.1016/j.lindif.2015.08.026.Google Scholar
  50. Kruger, J. (2002). Unskilled and unaware—but why? A reply to Krueger and Mueller. Journal of Personality and Social psychology, 82, 189–192.Google Scholar
  51. Kruger, J., & Dunning, D. (1999). Unskilled and unaware of it: How difficulties in recognizing one’s own incompetence lead to inflated self-assessments. Journal of Personality and Social Psychology, 77, 1121–1134.Google Scholar
  52. Lin, L., Moore, D., & Zabrucky, K. M. (2001). An assessment of student’s calibration of comprehension and calibration of performance using multiple measures. Reading Psychology, 22, 111–128.Google Scholar
  53. Lin, L., & Zabrucky, K. (1998). Calibration of comprehension: Research and implications for education and instruction. Contemporary Educational Psychology, 23, 345–391.Google Scholar
  54. Lin, L., Zabrucky, K. M., & Moore, D. (2002). Effects of text difficulty and adults’ age on relative calibration of comprehension. American Journal of Psychology, 115, 187–198.Google Scholar
  55. Lu, L., Weber, H. S., Spinath, F. M., & Shi, J. (2011). Predicting school achievement from cognitive and non-cognitive variables in a Chinese sample of elementary school children. Intelligence, 39(2–3), 130–140.  https://doi.org/10.1016/j.intell.2011.02.002.Google Scholar
  56. Lucangeli, D., Cornoldi, C., & Tellarini, M. (1998). Metacognition and learning disabilities in mathematics. In T. E. Scruggs & M. A. Mastropieri (Eds.), Advances in learning and behavioral disabilities (pp. 219–285). Greenwich: JAI Press Inc.Google Scholar
  57. Nelson, T. O. (1996). Consciousness and metacognition. American Psychologist, 51, 102–116.  https://doi.org/10.1037/0003-066X.51.2.102.Google Scholar
  58. Nietfeld, J. L., & Schraw, G. (2002). The role of knowledge and strategy training on metacognitive monitoring. The Journal of Educational Research, 95, 131–142.Google Scholar
  59. Orsini, C., Evans, P., & Jerez, O. (2015). How to encourage intrinsic motivation in the clinical teaching environment? A systematic review from the self-determination theory. Journal of Educational Evaluation for Health Professions, 12, 8.  https://doi.org/10.3352/jeehp.2015.12.8.Google Scholar
  60. Oszoy, G. (2011). An investigation of the relationship between metacognition and mathematics achievement. Asia Pacific Education Review, 12, 227–235.  https://doi.org/10.1007/s12564-010-9129-6.Google Scholar
  61. Ozcan, Z. C. (2014). Assessment of metacognition in mathematics: Which one of two methods is a better predictor of mathematics achievement? International Online Journal of Educational Studies, 6(1), 49–57.  https://doi.org/10.15345/iojes.2014.01.006.Google Scholar
  62. Perfect, T., & Schwartz, B. (2002). Applied metacognition. Cambridge: Cambridge University Press.Google Scholar
  63. Pieters, S., Roeyers, H., Rosseel, Y., Van Waelvelde, H., & Desoete, A. (2015). Identifying subtypes among children with developmental coordination disorder and mathematical learning disabilities, using model-based clustering. Journal of learning disabilities. 48(1), 83–95.  https://doi.org/10.1177/0022219413491288.Google Scholar
  64. Pressley, M. (2000). Development of grounded theories of complex cognitive processing: exhaustive within- and between study analyses of thinking-aloud data. In G. Schraw & J. C. Impara (Eds.), Issues in the measurement of metacognition (pp. 262–296). Lincoln: Buros Institute of Mental Measurements.Google Scholar
  65. Ryan, R. M., & Deci, E. L. (2017). Self-determination theory. Basic psychological needs in motivation, development and wellness. New York: Guilford Press.Google Scholar
  66. Schneider, W., & Artelt, C. (2010). Metacognition and mathematics education. ZDM: The International Journal on Mathematics Education, 42, 149–161.  https://doi.org/10.1007/s11858-010-0240-2.Google Scholar
  67. Schneider, W., & Löffler, E. (2016). The development of metacognitive knowledge in children and adolescents. In J. Dunlosky & S. K. Tauber (Eds.), The Oxford handbook of metamemory (pp. 491–518). New York: Oxford University Press.Google Scholar
  68. Schraw, G., Kuch, F., & Gutierrez, A. P. (2013). Measure for measure: Calibrating ten commonly used calibration scores. Learning and Instruction, 24, 48–57.Google Scholar
  69. Schraw, G., Kuch, F., Gutierrez, A. P., & Richmond, A. S. (2014). Exploring a three-level model of calibration accuracy. Journal of Educational Psychology, 106, 1192–1202.Google Scholar
  70. Seaton, M., Marsh, H. W., Parker, P. D., Craven, R. G., & Yeung, A. S. (2015). The Reciprocal Effects Model revisited. Gifted Child Quarterly, 59, 143–156.  https://doi.org/10.1177/0016986215583870.Google Scholar
  71. Siemann, J., & Petermann, F. (2018). Evaluation of the Triple Code Model of numerical processing—Reviewing past neuroimaging and clinical findings. Research in Developmental Disabilities, 72, 106–117.  https://doi.org/10.1016/j.ridd.2017.11.001.Google Scholar
  72. Sperling, R. A., Howard, B. C., Miller, L. A., & Murphy, C. (2002). Measures of children’s knowledge and regulation of cognition. Contemporary Educational Psychology, 27, 51–79.Google Scholar
  73. Spinath, B., Spinath, F. M., Harlaar, N., & Plomin, R. (2006). Predicting school achievement from general cognitive ability, self-perceived ability, and intrinsic value. Intelligence, 34, 363–374.  https://doi.org/10.1016/j.intell.2005.11.004.Google Scholar
  74. Stolp, S., & Zabrucky, K. M. (2009) Contributions of metacognitive and self regulated learning theories to investigations of calibration of comprehension. International Electronic Journal of Elementary Education, 2(1), 7–31.Google Scholar
  75. Tarricone, P. (2011). The taxonomy of metacognition. Hove: Psychology Press.Google Scholar
  76. Taylor, G., Jungert, T., Mageau, G. A., Schattke, K., Dedic, H., Rosenfield, S., & Koestner, R. (2014). A self-determination theory approach to predicting school achievement over time: The unique role of Intrinsic Motivation. Contemporary Educational Psychology, 39, 342–358.  https://doi.org/10.1016/j.cedpsych.2014.08.002.Google Scholar
  77. Townsend, C. L., & Heit, E. (2011). Jugdments of learning and improvement. Memory & Cognition, 39, 204–216.  https://doi.org/10.3758/s13421-010-0019-2.Google Scholar
  78. Vanderswalmen, R., Vrijders, J., & Desoete, A. (2010). Metacognition and spelling performance in college students. In A. Efklides & P. Misailidi (Eds.), Trends and prospects in metacognition research (pp. 367–394). New York: Springer.Google Scholar
  79. Vansteenkiste, M., Sierens, E., Soenens, B., Luyckx, K., & Lens, W. (2009). Motivational profiles from a self-determination perspective: The quality of motivation matters. Journal of Educational Psychology, 101, 671–688.  https://doi.org/10.1037/a0015083.Google Scholar
  80. Veenman, M. V. J. (2011). Alternative assessment of strategy use with self-report instruments: A discussion. Metacognition and Learning, 6, 205–211.  https://doi.org/10.1007/s11409-011-9080-x.Google Scholar
  81. Veenman, M. V. J., Van Hout-Wolters, B. H. A. M., & Afflerbach, P. (2006). Metacognition and learning: Conceptual and methodological considerations. Metacognition and Learning, 1, 3–14.Google Scholar
  82. Vermeer, H. J., Boekaerts, M., & Seegers, G. (2000). Motivational and gender differences: Sixth-grade students’ mathematical problem-solving behavior. Journal of Educational Psychology, 92, 308–315.  https://doi.org/10.1037/0022-0663.92.2.308.Google Scholar
  83. Verschaffel, L. (1999). Realistic mathematical modelling and problem solving in the upper elementary school: Analysis and improvement. In J. H. M. Hamers, J. E. H. Van Luit & B. Csapo (Eds.), Teaching and learning thinking skills. Contexts of learning (pp. 215–240). Lisse: Swets & Zeitlinger.Google Scholar
  84. Wang, A. H., Shen, F., & Byrnes, J. P. (2013). Does the opportunity–propensity framework predict the early mathematics skills of low-income pre-kindergarten children? Contemporary Educational Psychology, 38, 259–270.  https://doi.org/10.1016/j.cedpsych.2013.04.004.Google Scholar

Copyright information

© FIZ Karlsruhe 2018

Authors and Affiliations

  • Annemie Desoete
    • 1
    • 2
    Email author
  • Elke Baten
    • 1
  • Vera Vercaemst
    • 3
  • Ann De Busschere
    • 3
  • Myriam Baudonck
    • 3
  • Jennis Vanhaeke
    • 4
  1. 1.Department of Experimental Clinical and Health PsychologyGhent UniversityGhentBelgium
  2. 2.ArteveldehogeschoolGhentBelgium
  3. 3.Centre for Rehabilitation OverleieKortrijkBelgium
  4. 4.Libraro BrugesBruggeBelgium

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